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Date: I think it was made between 1970 and 2000.

The computer appears as a panel on a wall with blinking lights. Green ooze is seeping from it, it has been spliced with living tissue (?), which is what caused it to evolve and become sentient and see humans as a threat to it’s existence.

It killed people with the elevator (but it’s not about a killer elevator) and it could suck out the “energy” from people through telephones.
In one scene someone picked up the receiver of a telephone and he disappeared completely probably via some cheap animation effect. The “brain” of the computer consumed him as a form of energy to sustain itself.
In another scene, the bulletproof glass main doors of the building were closing and the people threw a chair between them but it disappeared.
They lived in constant fear, not knowing what can they touch without getting killed.

It’s not:

Demon Seed (1977)
Tron (1982)
Cross talk (1982)
The Lift (1983)
The Tower (1985)
The Tower (1993)
The Outer Limits – The Haven (1999)
Virus (1999)
The Shaft AKA Down (2001)
Resident Evil (2002)
666 Park Avenue (TV Series 2012-2013)

It’s an almost 7 year old question on another site.

Question is closed for new answers.
Selected answer as best

does the other question have any other details? i have found a couple ones not on this list, but no skyscrapers yet…. this seems like ghost in the machine or lawnmower man style flick from 80s and 90s. doubt those 2 are them, as “mangler 2” probably not either. there was “urge to kill” from 1989.

I summed it all up here, so there’s no more info at the moment. The OP once called it a category “D” Swedish movie but I don’t know how serious that remark was. I’ve found nothing using the Swedish angle.
I have looked into these movies before, except Mangler 2 but they don’t seem to have the energy draining phone.
I think it’s not necessarily a skyscraper, it could be an office building or an apartment complex but it has to be big enough to warrant an elevator.
Thanks for looking into it!

Just to throw another killer elevator/building horror movie in the mix:

The 13th Floor

https://www.imdb.com/title/tt0094591/

Dial:Help is italian about a killer energy in phone line thing stalking her in different places.

https://m.imdb.com/title/tt0095952/reviews?ref_=m_tt_urv

Murder by Phone (1982) seems less possible, specifically being all phone kills. There are a couple tv movies of security systems going haywire and killing, but i have to find the names again

Stonebroke:
The 13th Floor (1988) is available on YouTube so I skimmed through it and it carries some resemblance to my movie but it can’t be it.
Thanks for the tip though!

VHS_Lives:
Dial: Help (1988). This does have the killer-phone idea but the rest is different from what I’m looking for.
Murder by Phone (1982): This can’t be it either.
In the movie I’m looking for the act of killing via the receiver was an act of predation, the computer “consumed” the victim to sustain itself.
Thanks though, I find it promising that you are looking into it. Not to disparage other people’s efforts but you’ve cracked some tough nuts for me in the past.